Eddie Hearn hinted the British star, who was awarded an OBE this week, could face "big mouth" Jarrell Miller in New York instead of the Bronze Bomber.
Hearn confirmed he has been speaking to Wilder's co-manager Shelly Finkel as he is ready to make a deal, but has not made any progress.
He told Sky Sports: "I have been speaking to Shelly Finkel and it will remain private.
"I am ready to make a deal but I can't say that it's close, because it isn't.
"It all depends on if Wilder wants to be the undisputed champion. If he does, then we'll get the fight made. If he's not bothered, we'll swerve it."
But the promoter is certain that the 29-year-old champion will fight in the USA soon.
He added: "It is the only fight that we want. If we can't get that fight, we'll look at others.
"The American debut is imminent. I'd like the American debut to be against Wilder but, if not, fighting in New York against a New Yorker with a big mouth would make a lot of sense."
Miller, who weighs a menacing 22st, has labelled the British champion as a "boring Barbie Doll."
The pair first clashed in July at a US press conference when the mouthy New Yorker made a joke about AJ's mum.
Joshua has three heavyweight titles, but he added another accolade to his collection at Buckingham Palace on Thursday.
He was awarded an OBE by Prince Charles after he received an MBE in 2013 for claiming an Olympic gold at London 2012.
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